Nonlinear vibration of simply supported star-shaped auxetic cylindrical shell

IF 2.5 3区 工程技术 Q2 MECHANICS
N. Mohandesi, M. Fadaee, M. Talebitooti
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引用次数: 0

Abstract

The nonlinear dynamic behavior and primary resonance of star-shaped auxetic cylindrical shells for large deformations are considered. First, the extensional and bending stiffness matrices are introduced in a closed-form relation for the star-shaped auxetic pattern. For this end, Castigliano’s theorem as well as the homogenization technique are applied. According to the classical theory of thin shells, including von Karman’s nonlinear terms, the governing equations of a star-shaped auxetic cylindrical shell are extracted. The Runge–Kutta and multiple scale methods are employed to solve the nonlinear equations of motion of the auxetic cylindrical shell for the Navier-type boundary conditions. The accuracy and stability of solutions are examined by the finite element analysis. The effects of geometrical parameters of a star-shaped auxetic cylinder on its linear and nonlinear vibrations are investigated. The presented mathematical procedure for linear and nonlinear vibration behaviors of auxetic structures can be developed for other auxetic patterns, such as honeycomb, chiral and re-entrant ones.

简支星形辅助圆柱壳的非线性振动
考虑了大变形时星形辅助圆柱壳的非线性动力特性和主共振。首先,以封闭关系引入了星形结构的拉伸刚度矩阵和弯曲刚度矩阵。为此,应用了Castigliano定理和均匀化技术。根据经典薄壳理论,包括von Karman非线性项,提取了星形异形圆柱壳的控制方程。采用龙格-库塔法和多尺度法求解了在navier型边界条件下圆柱壳的非线性运动方程。通过有限元分析验证了解的准确性和稳定性。研究了星形消声圆柱几何参数对其线性和非线性振动的影响。本文所提出的消声结构线性和非线性振动行为的数学方法也适用于其他消声结构,如蜂窝结构、手性结构和重入结构。
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来源期刊
CiteScore
4.40
自引率
10.70%
发文量
234
审稿时长
4-8 weeks
期刊介绍: Archive of Applied Mechanics serves as a platform to communicate original research of scholarly value in all branches of theoretical and applied mechanics, i.e., in solid and fluid mechanics, dynamics and vibrations. It focuses on continuum mechanics in general, structural mechanics, biomechanics, micro- and nano-mechanics as well as hydrodynamics. In particular, the following topics are emphasised: thermodynamics of materials, material modeling, multi-physics, mechanical properties of materials, homogenisation, phase transitions, fracture and damage mechanics, vibration, wave propagation experimental mechanics as well as machine learning techniques in the context of applied mechanics.
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